By George K. Francis
Praise for George Francis's A Topological Picturebook:
Bravo to Springer for reissuing this detailed and gorgeous e-book! It not just reminds the older iteration of the pleasures of doing arithmetic via hand, but in addition exhibits the hot new release what ``hands on'' relatively means.
- John Stillwell, collage of San Francisco
The Topological Picturebook has taught a complete iteration of mathematicians to attract, to work out, and to think.
- Tony Robbin, artist and writer of Shadows of truth: The Fourth size in Relativity, Cubism, and smooth Thought
The vintage reference for a way to provide topological info visually, jam-packed with remarkable hand-drawn images of advanced surfaces.
- John Sullivan, Technische Universitat Berlin
A Topological Picturebook shall we scholars see topology because the unique discoverers conceived it: concrete and visible, freed from the formalism that burdens traditional textbooks.
- Jeffrey Weeks, writer of The form of Space
A Topological Picturebook is a visible banquet for somebody excited about mathematical pictures. Francis offers beautiful examples to construct one's "visualization muscles". even as, he explains the underlying rules and layout strategies for readers to create their very own lucid drawings.
- George W. Hart, Stony Brook University
In this choice of narrative gemstones and fascinating hand-drawn photos, George Francis demonstrates the chicken-and-egg dating, in arithmetic, of photograph and textual content. because the booklet was once first released, the case for images in arithmetic has been gained, and now it's time to examine their that means. A Topological Picturebook is still indispensable.
- Marjorie Senechal, Smith university and co-editor of the Mathematical Intelligencer
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Additional info for A Topological Picturebook
The algorithm used by Stephen Gray for these graphs of trigonometric polynomials is quite simple and works well though slowly in BASIC on an Apple. Originally, it took ten dedicated minutes in the dead of night on PLATO's Cyber73/CDC6500 timeshared mainframe. It was the convenience of the PLATO system and the uncommonly supportive personal environment that got me started in programming there rather than on a proper graphics setup. My computer novitiate thus was similar to what awaits current beginners in micro-computing.
CABLE KNOT AND COMPANION. Figure 14. In the same paper of Thurston, there were other knots to be drawn. The computer furnished remarkable stereographs of the knot twisting about a torus eight times as it goes around the long way thrice. But none of the views worked on its own except this one, which depends on conventional shading for its effect. Only the pen, and perusal of Escher's graphics, helped in designing the knot pair at the bottom. It was essential to depict a knot within a knot. Windows or cross sections would have detracted from the continuity.
A figure can be drawn directly on the acetate, using a line pattern or complete picture as an underlay. Ordinary drawing ink works; inks more specifically intended for drawing on film are more permanent. They contain an acid but can be erased with a suitable fluid, at least for a while. This is usually neater than xerography, but more time-consuming. Since the solvent of many inks will smear adjacent pigments already applied, I sometimes color on alternating sides of the sheet. When using several overlays, it pays to tape the sheets together, so that they fit correctly.
A Topological Picturebook by George K. Francis